If the perimeter of a semicircular field is 144m, then the diameter of the field is (take `pi = (22)/(7)`)

Options

A. 55m
B. 30 m
C. 28 m
D. 56m

Answer

To solve the problem, we need to find the diameter of a semicircular field given that its perimeter is 144 meters. We'll use the value of π as \( \frac{22}{7} \).

### Step-by-Step Solution:

1. **Understand the Perimeter of a Semicircle**:
The perimeter \( P \) of a semicircular field can be calculated using the formula:
\[ P = \pi r + 2r \]
where \( r \) is the radius of the semicircle. The term \( \pi r \) represents the curved part, and \( 2r \) represents the two straight edges (the diameter).

2. **Set Up the Equation**:
Given that the perimeter is 144 meters, we can set up the equation:
\[ \pi r + 2r = 144 \]

3. **Substitute the Value of π**:
Substitute \( \pi \) with \( \frac{22}{7} \):
\[ \frac{22}{7} r + 2r = 144 \]

4. **Combine the Terms**:
To combine the terms, we need a common denominator. Rewrite \( 2r \) as \( \frac{14r}{7} \):
\[ \frac{22r}{7} + \frac{14r}{7} = 144 \]
This simplifies to:
\[ \frac{36r}{7} = 144 \]

5. **Clear the Fraction**:
Multiply both sides by 7 to eliminate the fraction:
\[ 36r = 144 \times 7 \]
Calculate \( 144 \times 7 \):
\[ 36r = 1008 \]

6. **Solve for r**:
Divide both sides by 36 to find \( r \):
\[ r = \frac{1008}{36} \]
Simplifying this gives:
\[ r = 28 \text{ meters} \]

7. **Calculate the Diameter**:
The diameter \( d \) of the semicircle is given by:
\[ d = 2r \]
Substituting the value of \( r \):
\[ d = 2 \times 28 = 56 \text{ meters} \]

### Final Answer:
The diameter of the semicircular field is **56 meters**.

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